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A131895
a(n) = (n + 2)*(5*n + 1)/2.
2
1, 9, 22, 40, 63, 91, 124, 162, 205, 253, 306, 364, 427, 495, 568, 646, 729, 817, 910, 1008, 1111, 1219, 1332, 1450, 1573, 1701, 1834, 1972, 2115, 2263, 2416, 2574, 2737, 2905, 3078, 3256, 3439, 3627, 3820, 4018, 4221, 4429, 4642, 4860, 5083, 5311, 5544
OFFSET
0,2
COMMENTS
Row sums of triangle A131894.
Binomial transform of (1, 8, 5, 0, 0, 0, ...).
FORMULA
a(n) = a(n-1) + 5*n + 3 (with a(0)=1). - Vincenzo Librandi, Nov 23 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=9, a(2)=22. - Harvey P. Dale, Sep 11 2015
From Elmo R. Oliveira, Oct 22 2024: (Start)
G.f.: (1 + 6*x - 2*x^2)/(1 - x)^3.
E.g.f.: (1 + 8*x + 5*x^2/2)*exp(x). (End)
EXAMPLE
a(2) = 22 = sum of row 2 terms of triangle A131894: (11 + 6 + 5).
a(2) = 22 = (1, 2, 1) dot (1, 8, 5) = (1 + 16 + 5).
MAPLE
A131895:=n->(n+2)*(5*n+1)/2; seq(A131895(n), n=0..50); # Wesley Ivan Hurt, Mar 26 2014
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {1, 9, 22}, 50] (* Harvey P. Dale, Sep 11 2015 *)
PROG
(PARI) a(n)=(n+2)*(5*n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A131894.
Sequence in context: A154528 A130861 A049730 * A323221 A250730 A251285
KEYWORD
nonn,easy,changed
AUTHOR
Gary W. Adamson, Jul 24 2007
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Dec 04 2008
Simpler definition from Wesley Ivan Hurt, Mar 26 2014
STATUS
approved