cp's OEIS Frontend

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, ...

%I A292611 #27 Sep 25 2017 07:50:31
%S A292611 10,45,55,136,153,171,325,351,378,406,666,703,741,780,820,1225,1275,
%T A292611 1326,1378,1431,1485,2080,2145,2211,2278,2346,2415,2485,3321,3403,
%U A292611 3486,3570,3655,3741,3828,3916,5050,5151,5253,5356,5460,5565,5671,5778,5886,7381
%N 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, ...
%H A292611 Seiichi Manyama, <a href="/A292611/b292611.txt">Table of n, a(n) for n = 1..10000</a>
%F A292611 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.
%e A292611    k|              A292610(n)                 |              a(n)           |       Sum
%e A292611    ---------------------------------------------------------------------------------------
%e A292611    0|                                                                           (=    0)
%e A292611    1|                           1 +   3 +   6 =  10                             (=   10)
%e A292611    2|                    15 +  21 +  28 +  36 =  45 +  55                       (=  100)
%e A292611    3|              66 +  78 +  91 + 105 + 120 = 136 + 153 + 171                 (=  460)
%e A292611    4|       190 + 210 + 231 + 253 + 276 + 300 = 325 + 351 + 378 + 406           (= 1460)
%e A292611    5| 435 + 465 + 496 + 528 + 561 + 595 + 630 = 666 + 703 + 741 + 780 + 820     (= 3710)
%t A292611 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 *)
%Y A292611 Cf. A000217, A222716, A292610.
%K A292611 nonn
%O A292611 1,1
%A A292611 _Seiichi Manyama_, Sep 20 2017