OFFSET
0,2
COMMENTS
Binomial transform of quasi-finite sequence 1, 6, 20, 16, 0, 0, ... (0 continued).
a(n+1) is the sum of the first and last number at the bottom (2nd row) of each block in A172002, 3+4, 13+20, 39+56, ...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 16.
a(n) = A168582(2*n+1) .
G.f.: (1 + 3*x + 11*x^2 + x^3)/(1 - x)^4.
E.g.f.: (1/3)*(3 + 18*x + 30*x^2 + 8*x^3)*exp(x). - G. C. Greubel, Jul 26 2016
MATHEMATICA
Table[ (4*n+3)*(1+2*n^2)/3 , {n, 0, 25}] (* G. C. Greubel, Jul 26 2016 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 7, 33, 95}, 40] (* Harvey P. Dale, May 16 2019 *)
PROG
(Magma) [(4*n+3)*(1+2*n^2)/3 : n in [0..40]]; // Vincenzo Librandi, Aug 06 2011
(PARI) a(n)=(4*n+3)*(1+2*n^2)/3 \\ Charles R Greathouse IV, Jul 26 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Nov 30 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Mar 25 2010
STATUS
approved