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A308215
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a(n) is the multiplicative inverse of A001844(n+1) modulo A001844(n); where A001844 is the sequence of centered square numbers.
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4
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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
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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a(n) satisfies a(n)*(2*n*(n+1)+1) == 1 (mod 2*n*(n-1)+1).
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)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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