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A091435
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Array T(n,k) = n(n+k), read by antidiagonals.
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0
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0, 1, 0, 4, 2, 0, 9, 6, 3, 0, 16, 12, 8, 4, 0, 25, 20, 15, 10, 5, 0, 36, 30, 24, 18, 12, 6, 0, 49, 42, 35, 28, 21, 14, 7, 0, 64, 56, 48, 40, 32, 24, 16, 8, 0, 81, 72, 63, 54, 45, 36, 27, 18, 9, 0, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, 0, 121, 110, 99, 88, 77, 66, 55, 44, 33, 22, 11
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| P. De Geest, Palindromic Quasipronics of the form n(n+x)
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FORMULA
| G.f.: x*(1+x-2*x^2*y)/((1-x*y)^2*(1-x)^3). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 05 2004
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EXAMPLE
| {0}; {1,0}; {4,2,0}; {9,6,3,0}; {16,12,8,4,0}; {25,20,15,10,5,0}; {36,30,24,18,12,6,0}
a(5,3) = 40 because 5 * (5 + 3) = 5 * 8 = 40.
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MAPLE
| seq(seq((j-i)*j, i=0..j), j=0..14);
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CROSSREFS
| Columns: a(n, 0) = A000290(n), a(n, 1) = A002378(n), a(n, 2) = A005563(n), a(n, 3) = A028552(n), a(n, 4) = A028347(n+2), a(n, 5) = A028557(n), a(n, 6) = A028560(n), a(n, 7) = A028563(n), a(n, 8) = A028566(n). Diagonals: a(n, n-4) = A054000(n-1), a(n, n-3) = A014107(n), a(n, n-2) = A046092(n-1), a(n, n-1) = A000384(n), a(n, n) = A001105(n), a(n, n+1) = A014105(n), a(n, n+2) = A046092(n), a(n, n+3) = A014106(n), a(n, n+4) = A054000(n+1), a(n, n+5) = A033537(n). Also note that the sums of the antidiagonals = A002411.
Cf. A056536, A056537, A082156.
Sequence in context: A200496 A058546 A196774 * A118441 A111549 A022696
Adjacent sequences: A091432 A091433 A091434 * A091436 A091437 A091438
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Ross La Haye (rlahaye(AT)new.rr.com), Mar 02 2004
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 15 2004
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