A365417 Partial sums of A265036.

1, 5, 11, 18, 28, 42, 62, 86, 110, 133, 159, 193, 235, 279, 319, 356, 398, 452, 516, 580, 636, 687, 745, 819, 905, 989, 1061, 1126, 1200, 1294, 1402, 1506, 1594, 1673, 1763, 1877, 2007, 2131, 2235, 2328, 2434, 2568, 2720, 2864, 2984, 3091, 3213, 3367, 3541, 3705, 3841, 3962, 4100, 4274, 4470, 4654

Offset: 0

Author

Ray Chandler, Sep 03 2023

Keywords

• nonn
• easy

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-12,18,-18,12,-5,1).

Crossrefs

Cf. A265036.

Programs

Mathematica

Join[{1,5,11},LinearRecurrence[{5, -12, 18, -18, 12, -5, 1},{18, 28, 42, 62, 86, 110, 133},50]]

Formula

G.f.: (2*x^9 - 6*x^8 + 8*x^7 - 7*x^6 + 2*x^5 + 2*x^4 - 5*x^3 + 2*x^2 - 1)/((x - 1)^3*(x^2 - x + 1)^2).

a(n) = 5*a(n-1) - 12*a(n-2) + 18*a(n-3) - 18*a(n-4) + 12*a(n-5) - 5*a(n-6) + a(n-7) for n > 10.