A329523 a(n) = n * (binomial(n + 1, 3) + 1).
0, 1, 4, 15, 44, 105, 216, 399, 680, 1089, 1660, 2431, 3444, 4745, 6384, 8415, 10896, 13889, 17460, 21679, 26620, 32361, 38984, 46575, 55224, 65025, 76076, 88479, 102340, 117769, 134880, 153791, 174624, 197505, 222564, 249935, 279756, 312169, 347320, 385359, 426440
Offset: 0
Examples
Square array begins: (0), 1, 2, 3, 4, 5, ... A001477 0, (1), 3, 7, 14, 25, ... A004006 0, 1, (4), 11, 24, 45, ... A006527 0, 1, 5, (15), 34, 65, ... A006003 (partial sums of A005448) 0, 1, 6, 19, (44), 85, ... A005900 (partial sums of A001844) 0, 1, 7, 23, 54, (105), ... A004068 (partial sums of A005891) ... This sequence is the main diagonal of the array.
References
- E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), 142.
Links
- Kelvin Voskuijl, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Programs
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Magma
[ n*(Binomial(n+1,3)+1):n in [0..40]]; // Marius A. Burtea, Nov 15 2019
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Magma
R
:=PowerSeriesRing(Integers(), 41); [0] cat Coefficients(R!(x*(1-x+5*x^2-x^3)/(1-x)^5)); // Marius A. Burtea, Nov 15 2019 -
Mathematica
Table[n (Binomial[n + 1, 3] + 1), {n, 0, 40}] nmax = 40; CoefficientList[Series[x (1 - x + 5 x^2 - x^3)/(1 - x)^5, {x, 0, nmax}], x] LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 4, 15, 44}, 41]
Comments