A320614 Expansion of (1 + x^5) / ((1 - x^2) * (1 - x^3) * (1 - x^7)) in powers of x.

1, 0, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 6, 8, 8, 9, 10, 11, 12, 13, 15, 15, 17, 18, 19, 21, 22, 24, 25, 27, 28, 30, 32, 33, 36, 37, 39, 41, 43, 45, 47, 50, 51, 54, 56, 58, 61, 63, 66, 68, 71, 73, 76, 79, 81, 85, 87, 90, 93, 96, 99, 102, 106, 108, 112, 115, 118

Offset

0,6

Links

Table of n, a(n) for n=0..67.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,0,1,-1,0,-1,1).

Formula

Euler transform of length 10 sequence [0, 1, 1, 0, 1, 0, 1, 0, 0, -1].

G.f.: (1 - x^10) / ((1 - x^2) * (1 - x^3) * (1 - x^5) * (1 - x^7)) = (1-x+x^2-x^3+x^4) / ((1-x)^3*(1+x+x^2)*(1+x+x^2+x^3+x^4+x^5+x^6)).

a(n) = a(-7-n) for all n in Z.

Example

G.f. = 1 + x^2 + x^3 + x^4 + 2*x^5 + 2*x^6 + 3*x^7 + 3*x^8 + 4*x^9 + ...

Mathematica

a[ n_] := Quotient[ n^2 + 7 n - 9 Boole[Mod[n, 3] == 1], 42] + 1;

Prog

(PARI) {a(n) = (n^2 + 7*n - 9*(n%3==1))\42 + 1};
(PARI) {a(n) = my(m=max(n, -7-n)); polcoeff( (1 + x^5) / ((1 - x^2)*(1 - x^3)*(1 - x^7))+ x*O(x^m), m)};

Crossrefs

Sequence in context: A092982 A302930 A248868 * A030566 A007963 A137222

Adjacent sequences: A320611 A320612 A320613 * A320615 A320616 A320617

Keyword

nonn,easy

Author

Michael Somos, Oct 17 2018

Status

approved