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A037237 Expansion of (3 + x^2) / (1 - x)^4. 5
3, 12, 31, 64, 115, 188, 287, 416, 579, 780, 1023, 1312, 1651, 2044, 2495, 3008, 3587, 4236, 4959, 5760, 6643, 7612, 8671, 9824, 11075, 12428, 13887, 15456, 17139, 18940, 20863, 22912, 25091, 27404 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
This sequence is the partial sums of A058331. - J. M. Bergot, May 31 2012
LINKS
FORMULA
a(n) = Sum_{k=0..n} (2*(k+1)^2 + 1). - Mike Warburton, Jul 07 2007, Sep 07 2007
a(n) = (n+1)*(2*n^2 + 7*n + 9)/3. - R. J. Mathar, Mar 29 2010
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 21 2012
E.g.f.: (1/3)*(9 + 27*x + 15*x^2 + 2*x^3)*exp(x). - G. C. Greubel, Jul 22 2017
MATHEMATICA
CoefficientList[Series[(3+x^2)/(1-x)^4, {x, 0, 50}], x] (* Harvey P. Dale, Mar 06 2011 *)
LinearRecurrence[{4, -6, 4, -1}, {3, 12, 31, 64}, 40] (* Vincenzo Librandi Jun 21 2012 *)
PROG
(Magma) I:=[3, 12, 31, 64]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)- Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 21 2012
(PARI) x='x+O('x^50); Vec((3+x^2)/(1-x)^4) \\ G. C. Greubel, Jul 22 2017
CROSSREFS
Sequence in context: A131936 A009135 A131740 * A005718 A199231 A098500
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)