|
| |
|
|
A121722
|
|
A triangular form based on the Hex number recursion: a[n]=2*a[n-1]-a[n-1]+6: A003215 form as generalized to Integer m.
|
|
0
| |
|
|
1, 1, 2, 1, 4, 7, 1, 7, 13, 19, 1, 11, 21, 31, 41, 1, 16, 31, 46, 61, 76, 1, 22, 43, 64, 85, 106, 127, 1, 29, 57, 85, 113, 141, 169, 197, 1, 37, 73, 109, 145, 181, 217, 253, 289, 1, 46, 91, 136, 181, 226, 271, 316, 361, 406, 1, 56, 111, 166, 221, 276, 331, 386, 441, 496, 551
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| A solution for the general type for m held constant: a[n] = 2*a[n - 1] - a[n - 2] + m With first two values as {1,1+m}
|
|
|
FORMULA
| a(n,m) = 1 + m*n*(1 + n)/2
|
|
|
EXAMPLE
| 1
1, 2
1, 4, 7
1, 7, 13, 19
1, 11, 21, 31, 41
1, 16, 31, 46, 61, 76
|
|
|
MATHEMATICA
| f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == 2*a[n - 1] - a[n - 2] + m, a[0] == 1, a[1] == 1 + m}, a[n], n][[1]] // FullSimplify] a = Table[Table[1 + m*n*(1 + n)/2, {m, 0, n}], {n, 0, 10}]
|
|
|
CROSSREFS
| Cf. A003215, A005891, A001844, A005448, A002061.
Sequence in context: A071948 A193589 A187115 * A193591 A059579 A091320
Adjacent sequences: A121719 A121720 A121721 * A121723 A121724 A121725
|
|
|
KEYWORD
| nonn,uned
|
|
|
AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 08 2006
|
| |
|
|
