A350437 a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A006942).

0, 0, 1, 2, 3, 7, 12, 18, 31, 52, 92, 158, 269, 460, 786, 1350, 2317, 3969, 6798, 11643, 19952, 34197, 58601, 100410, 172042, 294791, 505143, 865589, 1483206, 2541480, 4354847, 7462119, 12786520, 21909974, 37543133, 64330800, 110232005, 188884671, 323657539, 554593317

Offset

0,4

Comments

The integers are displayed as in A006942, where a 7 is depicted by 3 segments. The negative integers are depicted by using 1 segment more for the minus sign.

Since the integer 0 is depicted by 6 segments, in order to avoid considering -0 in the case n = 7, a(7) is obtained by decreasing of a unit the result of the sum A331529(7) + A331529(6) = 12 + 7 = 19, i.e., a(7) = 19 - 1 = 18.

The same sequence is obtained when 7 and 9 are depicted respectively by 4 and 5 segments (A074458).

Links

Table of n, a(n) for n=0..39.

Index entries for linear recurrences with constant coefficients, signature (0,1,1,1,3,3,1).

Index entries for sequences related to calculator display

Index entries for sequences related to compositions

Formula

a(7) = 18, otherwise a(n) = A331529(n) + A331529(n-1).

G.f.: x^2*(1 + 2*x + 2*x^2 + 4*x^3 + 6*x^4 + 3*x^5 - x^7 - x^8 - 3*x^9 - 3*x^10 - x^11)/(1 - x^2 - x^3 - x^4 - 3*x^5 - 3*x^6 - x^7).

a(n) = a(n-2) + a(n-3) + a(n-4) + 3*a(n-5) + 3*a(n-6) + a(n-7) for n > 13.

Example

a(7) = 18 since -111, -77, -41, -14, -9, -6, 8, 12, 13, 15, 21, 31, 47, 51, 74, 117, 171 and 711 are displayed by 7 segments.
segments.
                       __   __                                      __
   __   |  |  |     __   |    |    __ |__|  |    __   | |__|    __ |__|
        |  |  |          |    |          |  |         |    |        __|
        (-111)          (-77)         (-41)          (-14)        (-9)
       __      __        __         __         __      __        __
   __ |__     |__|    |  __|     |  __|     | |__      __|  |    __|  |
      |__|    |__|    | |__      |  __|     |  __|    |__   |    __|  |
     (-6)      (8)     (12)       (13)       (15)       (21)      (31)
        __      __        __               __       __        __
  |__|    |    |__   |      | |__|    |  |   |    |   |  |      |  |  |
     |    |     __|  |      |    |    |  |   |    |   |  |      |  |  |
     (47)        (51)        (74)       (117)       (171)        (711)

Mathematica

P[x_]:=x^2+x^3+x^4+3x^5+3x^6+x^7; c[n_]:=Coefficient[Sum[P[x]^k, {k, Max[1, Ceiling[n/7]], Floor[n/2]}], x, n]; b[n_]:=c[n]-c[n-6]; (* A331529 *)
a[n_]:=If[n!=7, b[n]+b[n-1], 18]; Array[a, 40, 0]

Crossrefs

Cf. A006942, A074458, A331529.

Sequence in context: A302506 A228828 A061577 * A006488 A121430 A217379

Adjacent sequences: A350434 A350435 A350436 * A350438 A350439 A350440

Keyword

nonn,base,easy

Author

Stefano Spezia, Dec 31 2021

Status

approved