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A023536 Convolution of natural numbers with A023532. 3
1, 2, 4, 7, 10, 14, 19, 25, 31, 38, 46, 55, 65, 75, 86, 98, 111, 125, 140, 155, 171, 188, 206, 225, 245, 266, 287, 309, 332, 356, 381, 407, 434, 462, 490, 519, 549, 580, 612, 645, 679, 714, 750, 786, 823, 861, 900, 940, 981, 1023, 1066, 1110, 1155 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Vladimir Letsko, Dec 18 2016: (Start)

Also, a(n) is the number of possible values for the number of diagonals in a convex polyhedron with n+3 vertices.

Let v>4 denote the number of vertices of convex polyhedra. The set of possible numbers of diagonals is the union of sets {(k-1)(v-k-4), ..., (k-1)(v-(k+6)/2)}, where 1 <= k <= floor((sqrt(8v-15)-5)/2), and the set {(k-1)(v-k-4), ..., (v-3)(v-4)/2}, where k = floor((sqrt(8v-15)-3)/2). Note that cardinalities of all sets of this union excluding the last one are consecutive triangular numbers. (End)

LINKS

Vladimir Letsko, Table of n, a(n) for n = 1..500

FORMULA

a(n) = (n(n + 5) - 4 )/2 - Sum_{k=2..n} floor(1/2 + sqrt(2(k + 2))). - Jan Hagberg (jan.hagberg(AT)stat.su.se), Oct 16 2002

From Paul Barry, May 24 2004: (Start)

a(n) = (n+1)(n+2)/2 - Sum_{k=1..n+1} floor((sqrt(8k+1)-1)/2);

a(n) = Sum_{k=1..n+1} k-floor((sqrt(8k+1)-1)/2). (End)

CROSSREFS

Cf. A005230, A279681.

Sequence in context: A022776 A025704 A025710 * A196126 A024536 A177237

Adjacent sequences:  A023533 A023534 A023535 * A023537 A023538 A023539

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Corrected by Jan Hagberg (jan.hagberg(AT)stat.su.se), Oct 16 2002

STATUS

approved

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)