A353128 Antidiagonal sums of A353109.

0, 0, 1, 4, 10, 20, 35, 20, 39, 48, 57, 40, 61, 58, 68, 92, 59, 96, 105, 114, 79, 118, 106, 116, 149, 98, 153, 162, 171, 118, 175, 154, 164, 206, 137, 210, 219, 228, 157, 232, 202, 212, 263, 176, 267, 276, 285, 196, 289, 250, 260, 320, 215, 324, 333, 342, 235, 346

Offset

0,4

Links

Table of n, a(n) for n=0..57.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: x^2*(1 + 4*x + 10*x^2 + 20*x^3 + 35*x^4 + 20*x^5 + 39*x^6 + 48*x^7 + 55*x^9 + 32*x^10 + 41*x^11 + 18*x^12 - 2*x^13 - 19*x^15 + 105*x^17 + x^18 + 3*x^19 + 6*x^20 + 10*x^21 + 15*x^22 + 89*x^23 + 19*x^24 + 9*x^25 - 48*x^26)/((1 - x)^2*(1 + x + x^2)^2*(1 + x^3 + x^6)^2).

a(n) = 2*a(n-9) - a(n-18) for n > 18.

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {0, 0, 1, 4, 10, 20, 35, 20, 39, 48, 57, 40, 61, 58, 68, 92, 59, 96, 105}, 58]

Crossrefs

Cf. A004247, A010888, A353109, A353933.

Sequence in context: A301139 A008116 A301162 * A362072 A102533 A341133

Adjacent sequences: A353125 A353126 A353127 * A353129 A353130 A353131

Keyword

nonn,base,easy

Author

Stefano Spezia, Apr 24 2022

Status

approved