A176203 Triangle read by rows: T(n, k) = 16*binomial(n, k) - 15.
1, 1, 1, 1, 17, 1, 1, 33, 33, 1, 1, 49, 81, 49, 1, 1, 65, 145, 145, 65, 1, 1, 81, 225, 305, 225, 81, 1, 1, 97, 321, 545, 545, 321, 97, 1, 1, 113, 433, 881, 1105, 881, 433, 113, 1, 1, 129, 561, 1329, 2001, 2001, 1329, 561, 129, 1, 1, 145, 705, 1905, 3345, 4017, 3345, 1905, 705, 145, 1
Offset: 0
Examples
Triangle begins as: 1; 1, 1; 1, 17, 1; 1, 33, 33, 1; 1, 49, 81, 49, 1; 1, 65, 145, 145, 65, 1; 1, 81, 225, 305, 225, 81, 1; 1, 97, 321, 545, 545, 321, 97, 1; 1, 113, 433, 881, 1105, 881, 433, 113, 1; 1, 129, 561, 1329, 2001, 2001, 1329, 561, 129, 1; 1, 145, 705, 1905, 3345, 4017, 3345, 1905, 705, 145, 1;
Links
- G. C. Greubel, Rows n = 0..100 of the triangle, flattened
Crossrefs
Programs
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Magma
[16*Binomial(n, k) -15: k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 12 2020
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Maple
A176203:= (n,k) -> 16*binomial(n, k) -15; seq(seq(A176203(n, k), k = 0..n), n = 0.. 12); # G. C. Greubel, Mar 12 2020
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Mathematica
T[n_, m_, q]:= 2^q*(Binomial[n, m] -1) + 1; Table[T[n,m,4], {n,0,12}, {m,0,n} ]//Flatten (* modified by G. C. Greubel, Mar 12 2020 *) Table[16*Binomial[n, k] -15, {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Mar 12 2020 *) -
Sage
[[16*binomial(n, k) -15 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Mar 12 2020
Formula
T(n, m, q) = 2*T(n, m, q-1) - 1, with T(n, m, 0) = binomial(n, m) and q = 4.
From G. C. Greubel, Mar 12 2020: (Start)
T(n, k, q) = 2^q * binomial(n, k) - (2^q - 1), with q = 4.
Sum_{k=0..n} T(n, k, q) = 2^(n + q) - (n + 1)*(2^q - 1) (row sums). (End)
Extensions
Edited by G. C. Greubel, Mar 12 2020
Comments