A265407 Spironacci-style recurrence: a(0)=0, a(1)=1, a(n) = 2*a(n) XOR a(A265409(n)).

0, 1, 2, 4, 8, 16, 32, 64, 129, 259, 519, 1036, 2074, 4150, 8296, 16600, 33208, 66424, 132832, 265696, 531424, 1062880, 2125696, 4251521, 8502785, 17005825, 34011905, 68023301, 136047622, 272093206, 544188470, 1088378998, 2176753882, 4353515996, 8707015520, 17414063992, 34828160840, 69656354600, 139312643368

Offset

0,3

Comments

Spironacci-polynomials evaluated at X=2 over the field GF(2).

This is otherwise computed like A078510, which starts with a(0)=0 placed in the center of spiral (in square grid), followed by a(1) = 1, after which each term is a sum of two previous terms that are nearest when terms are arranged in a spiral, that is terms a(n-1) and a(A265409(n)), except here we first multiply the term a(n-1) by 2, and use carryless XOR (A003987) instead of normal addition.

Links

Antti Karttunen, Table of n, a(n) for n = 0..256

Formula

a(0)=0, a(1)=1; after which, a(n) = 2*a(n) XOR a(A265409(n)).

a(n) = A248663(A265408(n)).

Prog

(Scheme) ;; With memoization-macro definec.
(definec (A265407 n) (if (< n 2) n (A003987bi (* 2 (A265407 (- n 1))) (A265407 (A265409 n)))))
;; Where A003987bi computes bitwise-XOR as in A003987.

Crossrefs

Cf. A003987, A248663, A265408, A265409.

Cf. also A078510, A264977.

Sequence in context: A079845 A278995 A117302 * A023422 A084638 A157021

Adjacent sequences: A265404 A265405 A265406 * A265408 A265409 A265410

Keyword

nonn

Author

Antti Karttunen, Dec 13 2015

Status

approved