A350438 a(n) is the number of integers that can be represented in a 7-segment display by using only n segments (version A010371).

0, 0, 1, 1, 3, 6, 11, 14, 23, 39, 71, 118, 195, 317, 537, 906, 1533, 2550, 4261, 7119, 11973, 20073, 33650, 56277, 94286, 157960, 264843, 443656, 743269, 1244915, 2085970, 3494922, 5855965, 9810370, 16436113, 27536138, 46135634, 77295509, 129501787, 216963199, 363500178

Offset: 0

Author

Stefano Spezia, Dec 31 2021

Keywords

• nonn
• base
• easy

Comments

The integers are displayed as in A010371, where a 7 is depicted by 4 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 A331530(7) + A331530(6) = 7 + 8 = 15, i.e., a(7) = 15 - 1 = 14.

Examples

			a(7) = 14 since -111, -71, -41, -17, -14, -9, -6, 8, 12, 13, 15, 21, 31 and 51 are displayed by 7 segments.
                      __                              __
  __   |  |  |    __ |  |  |    __ |__|  |    __   | |  |    __   | |__|
       |  |  |          |  |          |  |         |    |         |    |
       (-111)        (-71)         (-41)          (-17)          (-14)
      __         __      __        __        __        __     __
  __ |__|    __ |__     |__|    |  __|    |  __|    | |__     __|  |
      __|       |__|    |__|    | |__     |  __|    |  __|   |__   |
    (-9)       (-6)     (8)      (12)      (13)      (15)      (21)
  __         __
  __|  |    |__   |
  __|  |     __|  |
   (31)       (51)
		

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,0,2,3,3,1).
• Index entries for sequences related to calculator display
• Index entries for sequences related to compositions

Crossrefs

Cf. A010371, A331530.

Programs

Mathematica

P[x_]:=x^2+2x^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]; (* A331530 *)
a[n_]:=If[n!=7,b[n]+b[n-1],14]; Array[a, 41, 0]

Formula

a(7) = 14, otherwise a(n) = A331530(n) + A331530(n-1).

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

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