VOOZH about

URL: https://oeis.org/A131924

⇱ A131924 - OEIS

login
A131924
Row sums of triangle A131923.
4
1, 4, 10, 20, 36, 62, 106, 184, 328, 602, 1134, 2180, 4252, 8374, 16594, 33008, 65808, 131378, 262486, 524668, 1048996, 2097614, 4194810, 8389160, 16777816, 33555082, 67109566, 134218484, 268436268, 536871782, 1073742754, 2147484640
OFFSET
0,2
FORMULA
Binomial transform of (1, 3, 3, 1, 1, 1, ...).
a(n) = 2^n + n^2 + n. - Michel Marcus, Jul 18 2018
From Colin Barker, Jul 18 2018: (Start)
G.f.: (1 - x - x^2 - x^3) / ((1 - x)^3*(1 - 2*x)).
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>3.
(End)
EXAMPLE
a(4) = 36 = sum of terms in row 4 of triangle A131923: (5 + 8 + 10 + 8 + 5).
a(4) = 36 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, 1) = (1 + 12 + 18 + 4 + 1).
MATHEMATICA
Table[2^n + n^2 + n, {n, 0, 5!}] (* Vladimir Joseph Stephan Orlovsky, May 07 2010 *)
LinearRecurrence[{5, -9, 7, -2}, {1, 4, 10, 20}, 40] (* Harvey P. Dale, Jul 22 2021 *)
PROG
(GAP) a:=List(List([0..32], n->List([0..n], k->Binomial(n, k)+n)), Sum); # Muniru A Asiru, Jul 17 2018
(PARI) Vec((1 - x - x^2 - x^3) / ((1 - x)^3*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Jul 18 2018
CROSSREFS
Cf. A131923.
Sequence in context: A008059 A145132 A063758 * A143982 A000749 A360046
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jul 29 2007
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, May 07 2010
STATUS
approved