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 A308215 a(n) is the multiplicative inverse of A001844(n+1) modulo A001844(n); where A001844 is the sequence of centered square numbers. 4
 0, 2, 12, 11, 39, 28, 82, 53, 141, 86, 216, 127, 307, 176, 414, 233, 537, 298, 676, 371, 831, 452, 1002, 541, 1189, 638, 1392, 743, 1611, 856, 1846, 977, 2097, 1106, 2364, 1243, 2647, 1388, 2946, 1541, 3261, 1702, 3592, 1871, 3939, 2048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The sequence explores the relationship between the terms of A001844, the sums of consecutive squares. The sequence is an interleaving of A054552 (a number spiral arm) and (A001844-n). The gap between the lower values of A308215 and the upper values of A308217 increase by 3n; each successive gap increasing by 6. LINKS Daniel Hoyt, Graph of A308215 and A308217 in relation to A001844 FORMULA a(n) satisfies a(n)*(2*n*(n+1)+1) == 1 (mod 2*n*(n-1)+1). Conjectures from Colin Barker, May 16 2019: (Start) G.f.: x*(2 + 12*x + 5*x^2 + 3*x^3 + x^4 + x^5) / ((1 - x)^3*(1 + x)^3). a(n) = (3 + (-1)^n + 2*(2+(-1)^n)*n + 2*(3+(-1)^n)*n^2) / 4 for n>0. a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6) for n>6. (End) PROG (Python 3) import gmpy2 sos = [] # sum of squares a=0 b=1 for i in range(50):     c = a**2 + b**2     sos.append(c)     a +=1     b +=1 ls = [] for i in range(len(sos)-1):     c = gmpy2.invert(sos[i+1], sos[i])     ls.append(int(c)) print(ls) (PARI) f(n) = 2*n*(n+1)+1; \\ A001844 a(n) = lift(1/Mod(f(n+1), f(n))); \\ Michel Marcus, May 16 2019 CROSSREFS Cf. A001844, A033951, A054552, A308217. Sequence in context: A216349 A280015 A245281 * A216478 A181060 A171446 Adjacent sequences:  A308212 A308213 A308214 * A308216 A308217 A308218 KEYWORD nonn AUTHOR Daniel Hoyt, May 15 2019 STATUS approved

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Last modified November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)