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

0,3

Links

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

Formula

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

Example

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;
  ;
  ...

Maple

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

Prog

(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

Crossrefs

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

Sequence in context: A224962 A173540 A336264 * A377092 A292599 A071487

Adjacent sequences: A070767 A070768 A070769 * A070771 A070772 A070773

Keyword

nonn,look,tabf

Author

Henry Bottomley, May 06 2002

Status

approved