A254363 a(n) = 4^n + 6*2^n + 3^(n+1) + 10.

20, 35, 77, 203, 605, 1955, 6677, 23723, 86765, 324275, 1231877, 4738043, 18396125, 71940995, 282882677, 1116985163, 4424500685, 17568076115, 69883311077, 278367837083, 1109978272445, 4429440153635, 17686354389077, 70651224045803, 282322365983405, 1128441973997555, 4511225627508677, 18037276107243323, 72126226025905565

Offset: 0

Author

Luciano Ancora, Jan 29 2015

Keywords

• nonn
• easy

Comments

This is the sequence of fourth terms of "third partial sums of m-th powers".

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Luciano Ancora, Demonstration of formulas, page 2.
• Luciano Ancora, Recurrence relations for partial sums of m-th powers.
• Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Crossrefs

Cf. A062709, A254362, A254364.

Programs

Mathematica

Table[4^n + 6*2^n + 3^(n + 1) + 10, {n, 0, 28}] (* Michael De Vlieger, Jan 30 2015 *)

PARI

vector(30, n, n--; 4^n + 6*2^n + 3^(n+1) + 10) \\ Colin Barker, Jan 30 2015

Formula

From Colin Barker, Jan 30 2015: (Start)

G.f.: -(342*x^3-427*x^2+165*x-20)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)).

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n > 3. (End)

E.g.f.: exp(x)*(exp(3*x) + 3*exp(2*x) + 6*exp(x) + 10). - Elmo R. Oliveira, Sep 12 2024