an interesting new sequence!

[N. J. A. Sloane]

Richard said:

The answer is   binom{n}{3}.  How is
it that when I searched OEIS (with
0 0 1 4 10 20 35 ) it only came up with
A101552 ??


Me:  The instructions are that when using the OEIS you should
always omit the first couple of terms - especially if they are 0 -
because people often have different opinions about where a sequence starts

The sequence you want is A000292:

%I A000292 M3382 N1363
%S A000292 0,1,4,10,20,35,56,84,120,165,220,286,364,455,560,680,816,969,1140,
%T A000292 1330,1540,1771,2024,2300,2600,2925,3276,3654,4060,4495,4960,5456,5984,
%U A000292 6545,7140,7770,8436,9139,9880,10660,11480,12341,13244,14190,15180
%N A000292 Tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6.
...

(the entry has 66 lines)

There is also an Index, which is often the
quickest way to find a common sequence which has a name
(e.g. the primes or the partition numbers)

Neil