A292611 Skip 3 triangle numbers, take 1 triangle number, skip 4 triangle numbers, take 2 triangle numbers, skip 5 triangle numbers, take 3 triangle numbers, ...

10, 45, 55, 136, 153, 171, 325, 351, 378, 406, 666, 703, 741, 780, 820, 1225, 1275, 1326, 1378, 1431, 1485, 2080, 2145, 2211, 2278, 2346, 2415, 2485, 3321, 3403, 3486, 3570, 3655, 3741, 3828, 3916, 5050, 5151, 5253, 5356, 5460, 5565, 5671, 5778, 5886, 7381

Offset

1,1

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

Sum_{n = (k-1)*k/2+1 .. k*(k+1)/2} a(n) = Sum_{n = (k+1)*(k+2)/2-2 .. (k+2)*(k+3)/2-3} A292610(n) = A222716(k+1) for k > 0.

Example

   k|              A292610(n)                 |              a(n)           |       Sum
   ---------------------------------------------------------------------------------------
   0|                                                                           (=    0)
   1|                           1 +   3 +   6 =  10                             (=   10)
   2|                    15 +  21 +  28 +  36 =  45 +  55                       (=  100)
   3|              66 +  78 +  91 + 105 + 120 = 136 + 153 + 171                 (=  460)
   4|       190 + 210 + 231 + 253 + 276 + 300 = 325 + 351 + 378 + 406           (= 1460)
   5| 435 + 465 + 496 + 528 + 561 + 595 + 630 = 666 + 703 + 741 + 780 + 820     (= 3710)

Mathematica

Block[{s = Array[{#, # + 3} &, 11] - 1, r}, r = PolygonalNumber@ Range@ Total@ Flatten@ s; Map[Function[{a, b}, {First@ #, Set[r, Drop[Last@ #, b]]} &@ TakeDrop[r, a]] @@ # &, s][[All, 1]] // Flatten] (* Michael De Vlieger, Sep 25 2017 *)

Crossrefs

Cf. A000217, A222716, A292610.

Sequence in context: A202296 A299530 A238982 * A275623 A245871 A199350

Adjacent sequences: A292608 A292609 A292610 * A292612 A292613 A292614

Keyword

nonn

Author

Seiichi Manyama, Sep 20 2017

Status

approved