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A174720
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Triangle T(n, k, q) = (1-q^n)*( binomial(n, k) - 1 ) + 1, with q = 4, read by rows.
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3
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1, 1, 1, 1, -14, 1, 1, -125, -125, 1, 1, -764, -1274, -764, 1, 1, -4091, -9206, -9206, -4091, 1, 1, -20474, -57329, -77804, -57329, -20474, 1, 1, -98297, -327659, -557021, -557021, -327659, -98297, 1, 1, -458744, -1769444, -3604424, -4521914, -3604424, -1769444, -458744, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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The row sums of this class of sequences, for varying q, is given by Sum_{k=0..n} T(n, k, q) = q^n * (n+1) + 2^n * (1 - q^n). - G. C. Greubel, Feb 09 2021
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LINKS
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FORMULA
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T(n, k, q) = (1-q^n)*( binomial(n, k) - 1 ) + 1, with q=4.
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, -14, 1;
1, -125, -125, 1;
1, -764, -1274, -764, 1;
1, -4091, -9206, -9206, -4091, 1;
1, -20474, -57329, -77804, -57329, -20474, 1;
1, -98297, -327659, -557021, -557021, -327659, -98297, 1;
1, -458744, -1769444, -3604424, -4521914, -3604424, -1769444, -458744, 1;
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MATHEMATICA
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T[n_, k_, q_]:= 1 +(1-q^n)*(Binomial[n, k] -1);
Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten
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PROG
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(Sage)
def T(n, k, q): return 1 + (1-q^n)*(binomial(n, k) - 1)
flatten([[T(n, k, 4) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 09 2021
(Magma)
T:= func< n, k, q | 1 + (1-q^n)*(Binomial(n, k) -1) >;
[T(n, k, 4): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 09 2021
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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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