A390418 Partial sums of A014829.

1, 9, 60, 370, 2235, 13431, 80614, 483720, 2902365, 17414245, 104485536, 626913294, 3761479855, 22568879235, 135413275530, 812479653316, 4874877920049, 29249267520465, 175495605122980, 1052973630738090, 6317841784428771, 37907050706572879, 227442304239437550, 1364653825436625600

Offset

1,2

Comments

Convolution of the powers of 6 with the triangular numbers [1, 3, 6, 10, ...].

Links

Table of n, a(n) for n=1..24.

Index entries for linear recurrences with constant coefficients, signature (9,-21,19,-6).

Formula

a(n) = (72*6^n - 25*n^2 - 85*n - 72)/250.

a(n) = 9*a(n-1) - 21*a(n-2) + 19*a(n-3) - 6*a(n-4), n >= 5.

G.f.: x/((1 - 6*x)*(1 - x)^3).

E.g.f.: exp(x)*(72*exp(5*x) - 25*x^2 - 110*x - 72)/250.

Apply partial sum operator thrice to A000400.

Mathematica

a[n_] := (72*6^n - 25*n^2 - 85*n - 72)/250; Array[a, 24] (* Amiram Eldar, Nov 06 2025 *)

Crossrefs

Cf. A000217, A000400, A003464, A014829.

Second partial sums of A003464.

Sequence in context: A385563 A026785 A153820 * A009139 A086018 A197402

Adjacent sequences: A390415 A390416 A390417 * A390419 A390420 A390421

Keyword

nonn,easy

Author

Enrique Navarrete, Nov 05 2025

Status

approved