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A153126
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Sums of rows of the triangle in A153125.
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6
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1, 6, 18, 33, 55, 80, 112, 147, 189, 234, 286, 341, 403, 468, 540, 615, 697, 782, 874, 969, 1071, 1176, 1288, 1403, 1525, 1650, 1782, 1917, 2059, 2204, 2356, 2511, 2673, 2838, 3010, 3185, 3367, 3552, 3744, 3939, 4141, 4346, 4558, 4773, 4995, 5220, 5452
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the line from 1, in the direction 1, 6,..., and the same line from 1, in the direction 1, 18,..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. Line perpendicular to the main axis A195015 in the same spiral. - Omar E. Pol, Oct 14 2011
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LINKS
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FORMULA
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a(n) = n*(5*n+7)/2 + 1 - n mod 2.
a(n) = Sum_{k=1..n+1} A153125(n+1,k).
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: (1+4*x+6*x^2-x^3)/((1-x)^3*(1+x)). (End)
Sum_{n>=0} 1/a(n) = 5/7 + 2*sqrt(1+2/sqrt(5))*Pi/21 + 2*sqrt(5)*log(phi)/21 + 5*log(5)/21 - 8*log(2)/21, where phi is the golden ratio (A001622). - Amiram Eldar, Aug 23 2022
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MATHEMATICA
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LinearRecurrence[{2, 0, -2, 1}, {1, 6, 18, 33}, 50] (* Harvey P. Dale, Apr 13 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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