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A307972 G.f. A(x) satisfies: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5*A(x)^2. 9
1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 9, 14, 21, 30, 41, 58, 86, 130, 195, 286, 416, 612, 915, 1380, 2076, 3102, 4627, 6932, 10452, 15818, 23931, 36148, 54600, 82642, 125435, 190724, 290116, 441282, 671512, 1023052, 1560780, 2383578, 3642117, 5567202, 8514254, 13031192, 19960712 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Shifts 5 places left when convolved with itself.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..5000

FORMULA

G.f.: 1/(1 - x/(1 - x^5/(1 - x^5/(1 - x/(1 - x^5/(1 - x^5/(1 - x/(1 - x^5/(1 - x^5/(1 - ...)))))))))), a continued fraction.

Recurrence: a(n+5) = Sum_{k=0..n} a(k)*a(n-k).

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + x^5 + 2*x^6 + 3*x^7 + 4*x^8 + 5*x^9 + 6*x^10 + ...

MAPLE

a:= proc(n) option remember; `if`(n<5, 1,

      add(a(j)*a(n-5-j), j=0..n-5))

    end:

seq(a(n), n=0..50);  # Alois P. Heinz, May 08 2019

MATHEMATICA

terms = 47; A[_] = 0; Do[A[x_] = 1 + x + x^2 + x^3 + x^4 + x^5 A[x]^2 + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

a[n_] := a[n] = Sum[a[k] a[n - k - 5], {k, 0, n - 5}]; a[0] = a[1] = a[2] = a[3] = a[4] = 1; Table[a[n], {n, 0, 47}]

CROSSREFS

Cf. A000108, A007477, A307970, A307971.

Sequence in context: A228669 A308020 A200444 * A346074 A211697 A211676

Adjacent sequences:  A307969 A307970 A307971 * A307973 A307974 A307975

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 08 2019

STATUS

approved

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)