A377521 Antidiagonal sums of A343053.

0, 0, 0, 15, 48, 115, 217, 385, 611, 945, 1366, 1947, 2650, 3575, 4663, 6045, 7637, 9605, 11836, 14535, 17556, 21147, 25125, 29785, 34903, 40825, 47282, 54675, 62686, 71775, 81571, 92597, 104425, 117645, 131768, 147455, 164152, 182595, 202161, 223665, 246411, 271297, 297550

Offset

0,4

Links

Table of n, a(n) for n=0..42.

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Formula

a(n) = (2 - n)*(12*(1 + (-1)^n) - 105*n + 3*(-1)^n*n - 32*n^2 - 4*n^3)/48 for n > 1.

a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8) for n > 9.

G.f.: x^3*(15 + 18*x - 11*x^2 - 19*x^3 + 9*x^4 + 7*x^5 - 3*x^6)/((1 - x)^5*(1 + x)^3).

E.g.f.: (1 - 3*x + 23*x^2/8 + x^3 + x^4/12)*cosh(x) - x*(81 - 72*x - 24*x^2 - 2*x^3)*sinh(x)/24 - 1 + 3*x.

Mathematica

LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 0, 0, 15, 48, 115, 217, 385, 611, 945}, 43]

Crossrefs

Cf. A343053.

Sequence in context: A156205 A065906 A370912 * A154060 A168305 A208155

Adjacent sequences: A377518 A377519 A377520 * A377522 A377523 A377524

Keyword

nonn,easy

Author

Stefano Spezia, Jan 03 2025

Status

approved