A140226 Binomial transform of [1, 3, 3, 1, 1, -1, 1, -1, 1, ...].
1, 4, 10, 20, 36, 60, 94, 140, 200, 276, 370, 484, 620, 780, 966, 1180, 1424, 1700, 2010, 2356, 2740, 3164, 3630, 4140, 4696, 5300, 5954, 6660, 7420, 8236, 9110, 10044, 11040, 12100, 13226, 14420
Offset: 0
Examples
a(5) = 36 = (1, 4, 6, 4, 1) dot (1, 3, 3, 1, 1) = (1 + 12 + 18 + 4 + 1).
Links
- E. Hetmaniok, M. Pleszczynski, I. Sobstyl, R. Witula, Kaprekar's transformations. Part II-numerical results and intriguing corollaries, Position Papers of the Federated Conference on Computer Science and Information Systems pp. 97-104, ACSIS, Vol. 6; DOI: 10.15439/2015F15.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Maple
1, seq((1/3)*n*(11+n^2),n=1..35); # Emeric Deutsch, Jun 03 2008
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Mathematica
CoefficientList[Series[(1+x^4)/(1-x)^4,{x,0,50}],x] (* or *) LinearRecurrence[{4,-6,4,-1},{1,4,10,20,36},50] (* Harvey P. Dale, Aug 17 2021 *) -
PARI
a(n)=max(n*(11 + n^2)/3,1) \\ Charles R Greathouse IV, Oct 19 2022
Formula
A007318 * [1, 3, 3, 1, 1, -1, 1, -1, 1, ...].
From Emeric Deutsch, Jun 03 2008: (Start)
a(n) = n*(11 + n^2)/3 for n >= 1.
G.f.: (1+x^4)/(1-x)^4. (End)
Extensions
More terms from Emeric Deutsch, Jun 03 2008