A377375 Antidiagonal sums of A342819.

0, 0, 0, 4, 11, 25, 42, 70, 101, 147, 196, 264, 335, 429, 526, 650, 777, 935, 1096, 1292, 1491, 1729, 1970, 2254, 2541, 2875, 3212, 3600, 3991, 4437, 4886, 5394, 5905, 6479, 7056, 7700, 8347, 9065, 9786, 10582, 11381, 12259, 13140, 14104, 15071, 16125, 17182, 18330, 19481, 20727

Offset

0,4

Links

Table of n, a(n) for n=0..49.

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = (n - 2)*(2*n^2 + 10*n - 3*(1 + (-1)^n))/12 for n > 1.

a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n > 7.

G.f.: x^3*(4 + 3*x - x^2 - 3*x^3 + x^4)/((1 - x)^4*(1 + x)^2).

E.g.f.: (1 - x + x^2 + x^3/6)*cosh(x) - x*(9 - 6*x - x^2)*sinh(x)/6 - 1 + x.

Mathematica

LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 0, 0, 4, 11, 25, 42, 70}, 50]

Crossrefs

Cf. A342819.

Sequence in context: A349569 A349570 A192597 * A181946 A176959 A115294

Adjacent sequences: A377372 A377373 A377374 * A377376 A377377 A377378

Keyword

nonn,easy

Author

Stefano Spezia, Dec 28 2024

Status

approved