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A061793
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a(n) = 25*n*(n + 1)/2 + 3.
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1
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3, 28, 78, 153, 253, 378, 528, 703, 903, 1128, 1378, 1653, 1953, 2278, 2628, 3003, 3403, 3828, 4278, 4753, 5253, 5778, 6328, 6903, 7503, 8128, 8778, 9453, 10153, 10878, 11628, 12403, 13203, 14028, 14878, 15753, 16653, 17578, 18528, 19503
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OFFSET
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0,1
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COMMENTS
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"If m is a triangular number, then so are 9*m+1, 25*m+3 and 49*m+6. (Euler, 1775)", see Burton in References. Note that A060544 is the same as 9*m+1 when m is triangular and that 9*(m*(m+1)/2)+1 is another formula for it.
Complementing the previous comment, with T(n) = A000217(n), 4*T(s)+1+s = T(2*s+1), 16*T(s)+3+2s = T(4*s+2) and 36*T(s)+6+3s = T(6*s+3) are special cases of the identity A000290(2*r)*T(s) + T(r) + r*s = T(2*r*s + r). - Charlie Marion, Mar 28 2018
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REFERENCES
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D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, p. 17.
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LINKS
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FORMULA
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MAPLE
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MATHEMATICA
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PROG
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(PARI) v=[]; for(n=0, 100, v=concat(v, 25*(n*(n+1)/2)+3)); v
(PARI) { for (n=0, 1000, write("b061793.txt", n, " ", 25*n*(n + 1)/2 + 3) ) } \\ Harry J. Smith, Jul 28 2009
(GAP) List([0..40], n->25*(n*(n+1)/2)+3); # Muniru A Asiru, Mar 30 2018
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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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EXTENSIONS
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STATUS
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approved
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