A363299 a(n) is the sum of the n-th powers of the terms of row 4 of Pascal's triangle.

5, 16, 70, 346, 1810, 9826, 54850, 312706, 1810690, 10601986, 62563330, 371185666, 2210336770, 13194911746, 78901035010, 472332468226, 2829699842050, 16961019183106, 101697395621890, 609909495824386, 3658357463318530, 21945746733400066, 131656888214355970, 789870960541958146

Offset

0,1

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (11,-34,24).

Formula

a(n) = 2 + 2*4^n + 6^n.

From Nathan L. Skirrow, Jun 25 2023: (Start)

G.f.: (5-39*x+64*x^2)/((1-x)*(1-4*x)*(1-6*x)).

E.g.f.: 2*e^x + 2*e^(4*x) + e^(6*x).

(End)

Example

a(2) = 1^2 + 4^2 + 6^2 + 4^2 + 1^2 = 1 + 16 + 36 + 16 + 1 = 70.

Mathematica

Table[6^n + 2*(4^n + 1), {n, 0, 24}] (* Amiram Eldar, May 27 2023 *)

Prog

(Python)
def A363299(n): return 2+(((1<<n+1)+3**n)<<n) # Chai Wah Wu, Jun 27 2023

Crossrefs

Cf. A007318.

Cf. A000012 (row 0), A007395 (row 1), A052548 (row 2), A115099 (row 3).

Sequence in context: A042087 A332470 A151465 * A151474 A138550 A363558

Adjacent sequences: A363296 A363297 A363298 * A363300 A363301 A363302

Keyword

nonn,easy

Author

J. Lowell, May 26 2023

Status

approved