A022878 -id:A022878

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A022877

a(n) = floor( a(n-1)/a(1) + a(n-3)/a(3) + a(n-5)/a(5) + ... ), for n >= 3 with a(1) = 1 and a(2) = 3.

+10
1

1, 3, 3, 3, 4, 5, 6, 8, 10, 13, 17, 22, 29, 38, 50, 66, 87, 115, 152, 200, 264, 349, 461, 609, 804, 1062, 1402, 1852, 2446, 3231, 4267, 5636, 7444, 9832, 12987, 17154, 22657, 29926, 39528, 52210, 68961, 91087, 120312, 158913, 209899, 277244

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Iain Fox, Table of n, a(n) for n = 1..9000

FORMULA

a(1)=1; a(2)=3; a(n) = floor(Sum_{i=1..floor(n/2)} a(n - (2*i-1))/a(2*i-1)). - Iain Fox, Oct 19 2018

a(n) ~ c * d^n, where d = 1.32084589099698002679195399789776925593378276999586161625509416650335137419... and c = 0.76500378031110004583172254717466388647997642917290688057501304595... - Vaclav Kotesovec, Oct 22 2018

MATHEMATICA

a[1]:=1; a[2]:=3; a[n_]:=Floor[Sum[Mod[i, 2] a[n-i]/a[i], {i, n-1}]]; Table[a[n], {n, 1, 15}] (* Iain Fox, Oct 19 2018 *)

PROG

(PARI) first(n) = my(res=vector(n)); for(x=1, n, res[x]=if(x<3, [1, 3][x], floor(sum(i=1, x-1, (i%2)*res[x-i]/res[i])))); res \\ Iain Fox, Oct 19 2018

CROSSREFS

Cf. A022859, A022865, A022871.

Cf. A022860, A022866, A022872, A022878.

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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