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A141402 Triangle T(n, k) = n^2 + (2*k*(n-k))^2, read by rows. 1
0, 1, 1, 4, 8, 4, 9, 25, 25, 9, 16, 52, 80, 52, 16, 25, 89, 169, 169, 89, 25, 36, 136, 292, 360, 292, 136, 36, 49, 193, 449, 625, 625, 449, 193, 49, 64, 260, 640, 964, 1088, 964, 640, 260, 64, 81, 337, 865, 1377, 1681, 1681, 1377, 865, 337, 81, 100, 424, 1124, 1864, 2404, 2600, 2404, 1864, 1124, 424, 100 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
T(n, k) = n^2 + (2*k*(n-k))^2.
Sum_{k=0..n} T(n, k) = n*(2*n^4 + 15*n^2 + 15*n -2)/15. - G. C. Greubel, Mar 30 2021
EXAMPLE
Triangle begins as:
0;
1, 1;
4, 8, 4;
9, 25, 25, 9;
16, 52, 80, 52, 16;
25, 89, 169, 169, 89, 25;
36, 136, 292, 360, 292, 136, 36;
49, 193, 449, 625, 625, 449, 193, 49;
64, 260, 640, 964, 1088, 964, 640, 260, 64;
81, 337, 865, 1377, 1681, 1681, 1377, 865, 337, 81;
100, 424, 1124, 1864, 2404, 2600, 2404, 1864, 1124, 424, 100;
MAPLE
A141402:= (n, k)-> n^2 + (2*k*(n-k))^2;
seq(seq(A141402(n, k), k=0..n), n=0..12); # G. C. Greubel, Mar 30 2021
MATHEMATICA
T[n_, k_]:= n^2 + (2*k*(n-k))^2;
Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten
PROG
(Magma) [n^2 + (2*k*(n-k))^2: k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 30 2021
(Sage) flatten([[n^2 + (2*k*(n-k))^2 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 30 2021
CROSSREFS
Sequence in context: A165267 A092159 A322258 * A276619 A145900 A278676
KEYWORD
nonn,easy,tabl
AUTHOR
Roger L. Bagula, Aug 03 2008
EXTENSIONS
Edited by G. C. Greubel, Mar 30 2021
STATUS
approved

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Last modified April 19 09:19 EDT 2024. Contains 371782 sequences. (Running on oeis4.)