VOOZH about

URL: https://oeis.org/A254363

⇱ A254363 - OEIS

login
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
OFFSET
0,1
COMMENTS
This is the sequence of fourth terms of "third partial sums of m-th powers".
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
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
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Jan 29 2015
STATUS
approved