A179901 -id:A179901 - cp's OEIS frontend

A179902 Row sums of triangle A179901.

1, 2, 5, 11, 23, 46, 87, 155, 261, 416, 641, 947, 1355, 1886

Offset: 1

Gary W. Adamson, Jul 31 2010

nonn

Conjectured mod 2 parity: (1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1,...)

			a(5) = 23 = sum of 5th row terms of triangle A179901: (1, + 4, + 6 + 8 + 4).

Cf. A179901.

Row sums of triangle A179901

A179000 Array T(n,k) read by antidiagonals: coefficient [x^k] of (1 + n*Sum_{i>=1} x^i)^2, k >= 0.

Original entry on oeis.org

1, 1, 2, 1, 4, 3, 1, 6, 8, 4, 1, 8, 15, 12, 5, 1, 10, 24, 24, 16, 6, 1, 12, 35, 40, 33, 20, 7, 1, 14, 48, 60, 56, 42, 24, 8, 1, 16, 63, 84, 85, 72, 51, 28, 9, 1, 18, 80, 112, 120, 110, 88, 60, 32, 10

Offset: 1

Gary W. Adamson, Jan 03 2011

Antidiagonal sums are in A136396.

			First few rows of the array:
  1   2   3   4   5   6   7   8   9  10  11  A000027
  1   4   8  12  16  20  24  28  32  36  40  A008574
  1   6  15  24  33  42  51  60  69  78  87  A122709
  1   8  24  40  56  72  88 104 120 136 152  A051062
  1  10  35  60  85 110 135 160 185 210 235
  1  12  48  84 120 156 192 228 264 300 336
  1  14  63 112 161 210 259 308 357 406 455
  1  16  80 144 208 272 336 400 464 528 592
  1  18  99 180 261 342 423 504 585 666 747
Row n=3 is generated by (1 + 3x + 3x^2 + 3x^3 + 3x^4 + ...)^2 = 1 + 6x + 15x^2 + 24x^3 + ..., for example.

Cf. A136396, A179901.

A179000 := proc(n,k) if k = 0 then 1; else 2*n+n^2*(k-1) ; end if; end proc: # R. J. Mathar, Jan 05 2011

T(n,0) = 1; T(n,k) = n*(2+n*(k-1)), k > 0. - R. J. Mathar, Jan 05 2011

cp's OEIS Frontend

A179902 Row sums of triangle A179901.

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