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A185874 Second accumulation array of A051340, by antidiagonals. 6
1, 3, 4, 6, 11, 10, 10, 21, 26, 20, 15, 34, 48, 50, 35, 21, 50, 76, 90, 85, 56, 28, 69, 110, 140, 150, 133, 84, 36, 91, 150, 200, 230, 231, 196, 120, 45, 116, 196, 270, 325, 350, 336, 276, 165, 55, 144, 248, 350, 435, 490, 504, 468, 375, 220, 66, 175, 306, 440, 560, 651, 700, 696, 630, 495, 286, 78, 209, 370, 540, 700, 833, 924, 960, 930, 825, 638, 364, 91, 246, 440, 650, 855, 1036, 1176, 1260, 1275, 1210, 1056, 806, 455, 105, 286, 516, 770, 1025, 1260, 1456, 1596, 1665, 1650, 1540, 1326, 1001, 560 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A member of the accumulation chain: A051340 < A141419 < A185874 < A185875 < A185876 < ... (See A144112 for the definition of accumulation array.)
LINKS
Johann Cigler, Some elementary observations on Narayana polynomials and related topics, arXiv:1611.05252 [math.CO], 2016. See p. 24.
FORMULA
T(n,k) = k*n*(n+1)*(2*n+3*k+1)/12 for k>=1, n>=1.
EXAMPLE
Northwest corner:
. 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
. 4, 11, 21, 34, 50, 69, 91, 116, 144, 175, ...
. 10, 26, 48, 76, 110, 150, 196, 248, 306, 370, ...
. 20, 50, 90, 140, 200, 270, 350, 440, 540, 650, ...
. 35, 85, 150, 230, 325, 435, 560, 700, 855, 1025, ...
. 56, 133, 231, 350, 490, 651, 833, 1036, 1260, 1505, ...
. 84, 196, 336, 504, 700, 924, 1176, 1456, 1764, 2100, ...
. 120, 276, 468, 696, 960, 1260, 1596, 1968, 2376, 2820, ...
. 165, 375, 630, 930, 1275, 1665, 2100, 2580, 3105, 3675, ...
. 220, 495, 825, 1210, 1650, 2145, 2695, 3300, 3960, 4675, ...
...
MATHEMATICA
f[n_, k_] := (1/12)*k*n*(1 + n)*(1 + 3*k + 2*n);
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[f[n - k + 1, k], {n, 14}, {k, n, 1, -1}] // Flatten
CROSSREFS
Row 1 to 5: A000217, A115056, 2*A140096, 10*A000096, 5*A059845.
Column 1 to 3: A000292, A051925, A267370 and 3*A005581.
Main diagonal: A117066.
Sequence in context: A061032 A091424 A092839 * A320688 A352734 A275418
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, Feb 05 2011
EXTENSIONS
Edited by Bruno Berselli, Jan 14 2016
STATUS
approved

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Last modified March 28 16:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)