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

Author

Seiichi Manyama, Sep 20 2017

Keywords

• nonn

Examples

			   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)
		

Links

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

Crossrefs

Cf. A000217, A222716, A292610.

Programs

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 *)

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.