A070770 b + c + d where b >= c >= d >= 0 ordered by b then c then d.

0, 1, 2, 3, 2, 3, 4, 4, 5, 6, 3, 4, 5, 5, 6, 7, 6, 7, 8, 9, 4, 5, 6, 6, 7, 8, 7, 8, 9, 10, 8, 9, 10, 11, 12, 5, 6, 7, 7, 8, 9, 8, 9, 10, 11, 9, 10, 11, 12, 13, 10, 11, 12, 13, 14, 15, 6, 7, 8, 8, 9, 10, 9, 10, 11, 12, 10, 11, 12, 13, 14, 11, 12, 13, 14, 15, 16, 12, 13, 14, 15, 16, 17, 18, 7

Offset: 0

Author

Henry Bottomley, May 06 2002

Keywords

• nonn
• look
• tabf

Examples

			Triangle begins:
  0,
  ;
  1;
  2, 3;
  ;
  2;
  3, 4;
  4, 5, 6;
  ;
  3;
  4, 5,
  5, 6, 7;
  6, 7, 8, 9;
  ;
  4;
  5, 6;
  6, 7,  8;
  7, 8,  9, 10;
  8, 9, 10, 11, 12;
  ;
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001477, A051162, A070771, A070772 for similar sequences with different numbers of terms summed.

Programs

Maple

seq(seq(seq(b+c+d,d=0..c),c=0..b),b=0..10); # Robert Israel, Jun 21 2018

PARI

for(x=0,5,for(y=0,x,for(z=0,y,print1(x+y+z", ")))) \\ Charles R Greathouse IV, Sep 17 2015

Python

from math import isqrt, comb
from sympy import integer_nthroot
def A070770(n): return (m:=integer_nthroot(6*(n+1),3)[0])+(a:=n>=comb(m+2,3))+(k:=isqrt(b:=(c:=n+1-comb(m+a+1,3))<<1))-((b<<2)<=(k<<2)*(k+1)+1)+c-2-comb(k+(b>k*(k+1)),2) # Chai Wah Wu, Dec 11 2024

Formula

a(n) = A056556(n) + A056557(n) + A056558(n).