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A104246 Minimal number of tetrahedral numbers (A000292(k) = k(k+1)(k+2)/6) needed to sum to n. 35
1, 2, 3, 1, 2, 3, 4, 2, 3, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 1, 2, 3, 4, 2, 3, 4, 5, 3, 4, 2, 3, 4, 5, 3, 1, 2, 3, 4, 2, 2, 3, 4, 3, 3, 2, 3, 4, 4, 3, 3, 4, 5, 4, 4, 2, 1, 2, 3, 3, 2, 3, 4, 4, 3, 3, 2, 3, 4, 4, 2, 3, 4, 5, 3, 3, 2, 3, 4, 4, 3, 4, 5, 5, 1, 2, 3, 4, 2, 3, 3, 2, 3, 4, 2, 3, 3, 4, 3, 4, 4, 3, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
According to Dickson, Pollock conjectures that a(n) <= 5 for all n. Watson shows that a(n) <= 8 for all n, and Salzer and Levine show that a(n) <= 5 for n <= 452479659. - N. J. A. Sloane, Jul 15 2011
If we use the greedy algorithm for this, we get A281367. - N. J. A. Sloane, Jan 30 2017
Could be extended with a(0) = 0, in analogy to A061336. Kim (2003, first row of table "d = 3" on p. 73) gives max {a(n)} = 5 as a "numerical result", but the value has no "* denoting exact values" (see Remark at end of paper), which means this could be incorrect. - M. F. Hasler, Mar 06 2017, edited Sep 22 2022
REFERENCES
Dickson, L. E., History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 1952, see p. 13.
LINKS
Hyun Kwang Kim, On regular polytope numbers, Proc. Amer. Math. Soc. 131 (2003), pp. 65-75.
N. J. A. Sloane, Transforms
G. L. Watson, Sums of eight values of a cubic polynomial, J. London Math. Soc., 27 (1952), 217-224.
Eric Weisstein's World of Mathematics, Tetrahedral Number
MAPLE
tet:=[seq((n^3-n)/6, n=1..20)];
LAGRANGE(tet, 8, 120); # the LAGRANGE transform of a sequence is defined in A193101. - N. J. A. Sloane, Jul 15 2011
PROG
(PARI) available on request. - M. F. Hasler, Mar 06 2017
(PARI)
seq(N) = {
my(a = vector(N, k, 8), T = k->(k*(k+1)*(k+2))\6);
for (n = 1, N,
my (k1 = sqrtnint((6*n)\8, 3), k2 = sqrtnint(6*n, 3));
while(n < T(k2), k2--); if (n == T(k2), a[n] = 1; next());
for (k = k1, k2, a[n] = min(a[n], a[n - T(k)] + 1))); a;
};
seq(102) \\ Gheorghe Coserea, Mar 14 2017
CROSSREFS
Cf. A000292 (tetrahedral numbers), A000797 (numbers that need 5 tetrahedral numbers).
See also A102795-A102806, A102855-A102858, A193101, A193105, A281367 (the "triangular nachos" numbers).
Cf. A061336 (analog for triangular numbers).
Sequence in context: A053610 A264031 A338482 * A281367 A007720 A129968
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Feb 26 2005
EXTENSIONS
Edited by N. J. A. Sloane, Jul 15 2011
Edited by M. F. Hasler, Mar 06 2017
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)