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A254363 a(n) = 4^n + 6*2^n + 3^(n+1) + 10. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

FORMULA

G.f.: -(342*x^3-427*x^2+165*x-20) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)). - Colin Barker, Jan 30 2015

a(n) = 10*a(n-1)-35*a(n-2)+50*a(n-3)-24*a(n-4). - Colin Barker, Jan 30 2015

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A062709, A254362, A254364.

Sequence in context: A024755 A048022 A255349 * A229356 A048066 A287055

Adjacent sequences:  A254360 A254361 A254362 * A254364 A254365 A254366

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Jan 29 2015

STATUS

approved

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Last modified September 26 16:27 EDT 2020. Contains 337374 sequences. (Running on oeis4.)