A320603 a(0) = 1; if n is odd, a(n) = Product_{i=0..n-1} a(i); if n is even, a(n) = Sum_{i=0..n-1} a(i).

1, 1, 2, 2, 6, 24, 36, 20736, 20808, 8947059130368, 8947059171984, 716210897494804754044764041567551881216, 716210897494804754044764059461670225184

Offset

0,3

Comments

Next term is too large to include.

Odd terms are the product of previous terms and even terms are the sum of previous terms.

Links

Iain Fox, Table of n, a(n) for n = 0..18

Iain Fox, Table of n, a(n) for n = 0..32

Formula

a(n) = a(n-1) + 2*a(n-2), for even n > 2.

a(n) = a(n-1) * a(n-2)^2, for odd n > 1.

Example

5 is odd, so a(5) = 1 * 1 * 2 * 2 * 6 = 24.
6 is even, so a(6) = 1 + 1 + 2 + 2 + 6 + 24 = 36.

Mathematica

a[0]:= 1; a[n_]:= If[OddQ[n], Product[a[j], {j, 0, n-1}], Sum[a[j], {j, 0, n -1}]]; Table[a[n], {n, 0, 15}] (* G. C. Greubel, Oct 19 2018 *)

Prog

(PARI) first(n) = my(res = vector(n, i, 1)); for(x=3, n, res[x]=if(x%2, sum(i=1, x-1, res[i]), prod(i=1, x-1, res[i]))); res
(PARI) first(n) = my(res = vector(n, i, 1)); res[3]++; for(x=4, n, res[x]=if(x%2, res[x-1]+2*res[x-2], res[x-1]*res[x-2]^2)); res

Crossrefs

Cf. A039941, A077753, A122961.

Sum of previous terms: A011782.

Product of previous terms: A165420.

Sequence in context: A143084 A188962 A076741 * A276409 A093453 A301381

Adjacent sequences: A320600 A320601 A320602 * A320604 A320605 A320606

Keyword

nonn

Author

Iain Fox, Oct 17 2018

Status

approved