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A176228
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Triangle read by rows: T(n,k) = binomial(n,k) + Fibonacci(n) + 1.
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1
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2, 3, 3, 3, 4, 3, 4, 6, 6, 4, 5, 8, 10, 8, 5, 7, 11, 16, 16, 11, 7, 10, 15, 24, 29, 24, 15, 10, 15, 21, 35, 49, 49, 35, 21, 15, 23, 30, 50, 78, 92, 78, 50, 30, 23, 36, 44, 71, 119, 161, 161, 119, 71, 44, 36, 57, 66, 101, 176, 266, 308, 266, 176, 101, 66, 57
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OFFSET
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0,1
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COMMENTS
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Row sums are: {2, 6, 10, 20, 36, 68, 127, 240, 454, 862, 1640, ...}.
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LINKS
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FORMULA
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T(n, k) = binomial(n, k) + Fibonacci(n) + 1.
G.f.: 1/((-1 + x)*(-1 + y)) + x/((-1 + x + x^2)*(-1 + y)) + 1/(1 - x*(1 + y)). - Stefano Spezia, Nov 22 2019
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EXAMPLE
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Triangle begins as:
2;
3, 3;
3, 4, 3;
4, 6, 6, 4;
5, 8, 10, 8, 5;
7, 11, 16, 16, 11, 7;
10, 15, 24, 29, 24, 15, 10;
15, 21, 35, 49, 49, 35, 21, 15;
23, 30, 50, 78, 92, 78, 50, 30, 23;
36, 44, 71, 119, 161, 161, 119, 71, 44, 36;
57, 66, 101, 176, 266, 308, 266, 176, 101, 66, 57;
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MAPLE
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with(combinat); seq(seq(binomial(n, k) +fibonacci(n) +1, k=0..n), n=0..12); # G. C. Greubel, Nov 22 2019
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MATHEMATICA
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T[n_, k_]:= Binomial[n, k] + Fibonacci[n] + 1; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(PARI) T(n, k) = binomial(n, k)+fibonacci(n)+1; \\ G. C. Greubel, Nov 22 2019
(Magma) [Binomial(n, k)+Fibonacci(n)+1: k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 22 2019
(Sage) [[binomial(n, k)+fibonacci(n)+1 for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 22 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, k)+Fibonacci(n) +1))); # G. C. Greubel, Nov 22 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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